\(\Leftrightarrow1-sin2x+cos^3x-sin^3x=0\)
\(\Leftrightarrow\left(cosx-sinx\right)^2+\left(cosx-sinx\right)\left(1+sinx.cosx\right)=0\)
\(\Leftrightarrow\left(cosx-sinx\right)\left(cosx-sinx+1+sinx.cosx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=cosx\Leftrightarrow x=\frac{\pi}{4}+k\pi\\cosx-sinx+sinx.cosx+1=0\left(1\right)\end{matrix}\right.\)
Xét (1), đặt \(cosx-sinx=t\Rightarrow\left\{{}\begin{matrix}\left|t\right|\le\sqrt{2}\\sinx.cosx=\frac{1-t^2}{2}\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow t+\frac{1-t^2}{2}+1=0\)
\(\Leftrightarrow-t^2+2t+3=0\Rightarrow\left[{}\begin{matrix}t=-1\\t=3\left(l\right)\end{matrix}\right.\)
\(\Leftrightarrow\sqrt{2}cos\left(x+\frac{\pi}{4}\right)=-1\)
\(\Leftrightarrow cos\left(x+\frac{\pi}{4}\right)=-\frac{\sqrt{2}}{2}\)
\(\Leftrightarrow...\)
